On the Gibbs states for one-dimensional lattice Boson systems with a long-range interaction

E. Olivieri, P. Picco, Iouri M. Soukhov

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We consider an infinite chain of interacting quantum (anharmonic) oscillators. The pair potential for the oscillators at lattice distance d is proportional to {d2[log(d+1)]F(d)}-1 where ∑r∈Z [rF(r)]-1 < ∞. We prove that for any value of the inverse temperature β> 0 there exists a limiting Gibbs state which is translationally invariant and ergodic. Furthermore, it is analytic in a natural sense. This shows the absence of phase transitions in the systems under consideration for any value of the thermodynamic parameters.

Original languageEnglish (US)
Pages (from-to)985-1028
Number of pages44
JournalJournal of Statistical Physics
Issue number3-4
Publication statusPublished - Feb 1 1993


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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